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Author : Karel Hrbacek
Release : 1984
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Introduction to Set Theory by : Karel Hrbacek
Download or read book Introduction to Set Theory written by Karel Hrbacek. This book was released on 1984. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John P. Burgess
Release : 2022-03-10
Genre : Philosophy
Kind : eBook
Book Rating : 053/5 ( reviews)
Book Synopsis Set Theory by : John P. Burgess
Download or read book Set Theory written by John P. Burgess. This book was released on 2022-03-10. Available in PDF, EPUB and Kindle. Book excerpt: Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.
Author : Michael Potter
Release : 2004-01-15
Genre : Philosophy
Kind : eBook
Book Rating : 432/5 ( reviews)
Book Synopsis Set Theory and its Philosophy by : Michael Potter
Download or read book Set Theory and its Philosophy written by Michael Potter. This book was released on 2004-01-15. Available in PDF, EPUB and Kindle. Book excerpt: Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Author : Abhijit Dasgupta
Release : 2013-12-11
Genre : Mathematics
Kind : eBook
Book Rating : 540/5 ( reviews)
Book Synopsis Set Theory by : Abhijit Dasgupta
Download or read book Set Theory written by Abhijit Dasgupta. This book was released on 2013-12-11. Available in PDF, EPUB and Kindle. Book excerpt: What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.
Author : Joseph Breuer
Release : 2012-08-09
Genre : Mathematics
Kind : eBook
Book Rating : 874/5 ( reviews)
Book Synopsis Introduction to the Theory of Sets by : Joseph Breuer
Download or read book Introduction to the Theory of Sets written by Joseph Breuer. This book was released on 2012-08-09. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
